Holomorphic function

Holomorphic functions are the central object of study of complex analysis; they are functions defined on an open subset of the complex number plane C with values in C that are complex-differentiable at every point. This is a much stronger condition than real differentiability and implies that the function is infinitely often differentiable and can be described by its Taylor series. The term analytic function is often used interchangeably with "holomorphic function", although note that the former term has several other meanings. A function that is holomorphic on the whole complex plane is called an entire function. The phrase "holomorphic at a point a" means not just differentiable at a, but differentiable everywhere within some open disk centered at a in the complex plane. Biholomorphic means a holomorphic function with a holomorphic inverse function.

Related Topics:
Complex analysis - Functions - Open subset - Complex number plane - Real differentiability - Infinitely often differentiable - Taylor series - Analytic function - Entire function - Inverse function

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